Expression of type ExprTuple

from the theory of proveit.linear_algebra.scalar_multiplication

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprTuple, K, Lambda, Q, V, f, j, k
from proveit.core_expr_types import Q__b_1_to_j, b_1_to_j, f__b_1_to_j
from proveit.linear_algebra import ScalarMult, VecSpaces, VecSum
from proveit.linear_algebra.addition import vec_summation_b1toj_fQ
from proveit.logic import Equals, Forall, Implies, InSet
from proveit.numbers import NaturalPos

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([K, f, Q], Forall(instance_param_or_params = [j], instance_expr = Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [k], instance_expr = Implies(InSet(vec_summation_b1toj_fQ, V), Equals(ScalarMult(k, vec_summation_b1toj_fQ), VecSum(index_or_indices = [b_1_to_j], summand = ScalarMult(k, f__b_1_to_j), condition = Q__b_1_to_j)).with_wrapping_at(1)).with_wrapping_at(2), domain = K), domain = VecSpaces(K)), domain = NaturalPos)))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(K, f, Q\right) \mapsto \left[\forall_{j \in \mathbb{N}^+}~\left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{k \in K}~\left(\begin{array}{c} \begin{array}{l} \left(\left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right] \in V\right) \Rightarrow  \\ \left(\begin{array}{c} \begin{array}{l} \left(k \cdot \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right]\right) \\  = \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(k \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right)\right] \end{array} \end{array}\right) \end{array} \end{array}\right)\right]\right]\right]\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	35, 59, 58
3	Operation	operator: 18 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 64 body: 7
6	ExprTuple	64
7	Conditional	value: 8 condition: 9
8	Operation	operator: 18 operand: 12
9	Operation	operator: 36 operands: 11
10	ExprTuple	12
11	ExprTuple	64, 13
12	Lambda	parameter: 40 body: 15
13	Literal
14	ExprTuple	40
15	Conditional	value: 16 condition: 17
16	Operation	operator: 18 operand: 22
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22
20	Literal
21	ExprTuple	40, 23
22	Lambda	parameter: 56 body: 25
23	Operation	operator: 26 operand: 35
24	ExprTuple	56
25	Conditional	value: 28 condition: 29
26	Literal
27	ExprTuple	35
28	Operation	operator: 30 operands: 31
29	Operation	operator: 36 operands: 32
30	Literal
31	ExprTuple	33, 34
32	ExprTuple	56, 35
33	Operation	operator: 36 operands: 37
34	Operation	operator: 38 operands: 39
35	Variable
36	Literal
37	ExprTuple	45, 40
38	Literal
39	ExprTuple	41, 42
40	Variable
41	Operation	operator: 53 operands: 43
42	Operation	operator: 47 operand: 46
43	ExprTuple	56, 45
44	ExprTuple	46
45	Operation	operator: 47 operand: 50
46	Lambda	parameters: 60 body: 49
47	Literal
48	ExprTuple	50
49	Conditional	value: 51 condition: 55
50	Lambda	parameters: 60 body: 52
51	Operation	operator: 53 operands: 54
52	Conditional	value: 57 condition: 55
53	Literal
54	ExprTuple	56, 57
55	Operation	operator: 58 operands: 60
56	Variable
57	Operation	operator: 59 operands: 60
58	Variable
59	Variable
60	ExprTuple	61
61	ExprRange	lambda_map: 62 start_index: 63 end_index: 64
62	Lambda	parameter: 68 body: 65
63	Literal
64	Variable
65	IndexedVar	variable: 66 index: 68
66	Variable
67	ExprTuple	68
68	Variable